Research Interests
In Linear Algebra, I am mainly interested in spectral properties of matrix valued functions. Most of my work is devoted to the study of degeneracies (coalescence of eigenvalues or singular values, loss of rank) for matrices that depend on parameters, and of their effect on the associated subspaces. Numerical tools developed in my works include algorithms for smoothly computing eigendecomposition, SVD and Berry phase for matrix functions of one parameter and for detecting degeneracies (e.g., conical intersections) for functions of two or more parameters.
In Dynamical Systems, my main interest is on the numerical computation of, and the detection of bifurcations on, surfaces of equilibria. I have also done work on blow up or extinction in finite time for solutions of ODEs.
Recent/selected papers (published, accepted, or preprints)
Cusp bifurcations: numerical detection via two-parameter continuation and computer-assisted proofs of existence
JP Lessard, A Pugliese
arXiv:2404.00535, 2024
SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters
L Dieci, A Pugliese
arXiv:2402.14689, 2024
Takagi factorization of matrices depending on parameters and locating degeneracies of singular values
L Dieci, A Papini, A Pugliese
SIAM Journal on Matrix Analysis and Applications, 2022, DOI: 10.1137/21m1456273
Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters
L Dieci, A Papini, A Pugliese
Numerical Algorithms, 2022, DOI: 10.1007/s11075-022-01326-7
A note on the Kuramoto-Sivashinsky equation with discontinuity
L D'Ambrosio, M Gallo, A Pugliese
Mathematics in Engineering, 2021, DOI: 10.3934/mine.2021041
Coalescing points for eigenvalues of banded matrices depending on parameters with application to banded random matrix functions
L Dieci, A Papini, A Pugliese
Numerical Algorithms, 2019, DOI: 10.1007/s11075-018-0525-z
Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems
A Colombo, N Del Buono, L Lopez, A Pugliese
Discrete and Continuous Dynamical Systems - series B, 2018, DOI: 10.3934/DCDSB.2018166
Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions
M Gameiro, JP Lessard, A Pugliese
Foundations of Computational Mathematics, 2016, DOI: 10.1007/s10208-015-9259-7
Blow-up profile for solutions of a fourth order nonlinear equation
L D'Ambrosio, JP Lessard, A Pugliese
Nonlinear Analysis: Theory, Methods & Applications, 2015, DOI: 10.1016/J.NA.2014.12.026
Hermitian matrices of three parameters: perturbing coalescing eigenvalues and a numerical method
L Dieci, A Pugliese
Mathematics of Computation, 2015, DOI: 10.1090/mcom/2977
Approximating Coalescing Points for Eigenvalues of Hermitian Matrices of Three Parameters
L Dieci, A Papini, A Pugliese
SIAM Journal on Matrix Analysis and Applications, 2013, DOI: 10.1137/120898036
Hermitian matrices depending on three parameters: Coalescing eigenvalues
L Dieci, A Pugliese
Linear algebra and its applications, 2012, DOI: 10.1016/J.LAA.2012.01.009
Locating coalescing singular values of large two-parameter matrices
L Dieci, MG Gasparo, A Papini, A Pugliese
Mathematics and Computers in Simulation, 2011, DOI: 10.1016/j.matcom.2010.10.005
Two-Parameter SVD: Coalescing Singular Values and Periodicity
L Dieci, A Pugliese
SIAM Journal on Matrix Analysis and Applications, 2009, DOI: 10.1137/07067982X
Singular values of two-parameter matrices: an algorithm to accurately find their intersections
L Dieci, A Pugliese
Mathematics and Computers in Simulation, 2008, DOI: 10.1016/j.matcom.2008.03.012